1.A certain code consists of 5 variables,with each variable having 4 different constant values possible.What is the total number of coded messages that can be sent with 5 constants one from each variable?

2Akshay is planning to give a birthday party at his place.In how many ways can he invite one or more of five friends and seat  them at a circular table?Also in how many ways can he invite one or more of his five friends and seat them at a circular table with him?

3.How many ways are there to pick two different cards from a deck of 52 cards such that the first card is a spade and the second is not a queen?

4.There are 8 different locks,with exactly one key for each lock.All the keys have been mixed up.What is the maximum number of trials required in order to detremine which key belongs to which lock?

5.The total number of ways in which six "+" and four "-" signs can be arranged in a line such that no two "-" signs occur together?

6.Let A be the set of 4 digit numbers a1,a2,a3,a4 where a1>a2>a3>a4 then how many values of A are possible?

7.The total number of selections of atmost "n" things from "2n+1" different things is 63.What is the value of "n"?

8.The total number of integral solutions for (x,y,z) such that xyz=24 is?

9.The number of positive integral solutions of x+y+z = n,n E N,n>=3 is ?

10.There are 20 questions in a qn paper.If no two students solve the same combination of qns but solve equal number of qns,then the maximum number of students who appeared in the exam is ?

11.In how many ways can 15 isc and 13 bsc students be arranged in a line so that no two bsc students may occupy consecutive positions is?

12.How many numbers greater than 4 millions can be formed with the digits 2,3,0,4,3,2,5?

13.How many signals can be made by hoisting 2 blue, 2 red and 5 black flags on a pole at the same time?

14.In how many ways can 12 different books be distributed equally among 4 persons?

15.Find the sum of all the four digit numbers that can be formed with the digits 3,2,3,4?

16.The sides of a triangle have 3,4,5 interior points respectively on them .Find the number of triangles that can be constructed using given interior points as vertices?

17.Let S be the set of five-digit numbers formed by digits 1,2,3,,4 and 5 using each digit exactly once such that exactly 2 odd positions are occupied by odd digits.What is the sum of the digits in the rightmost position of the numbers in S?

18.A person wishes to throw as many different parties as he can out of his 20 friends such that each party consists of the same number of persons.The number of friends he should invite at a time is?